We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the log-likelihood under each model, from which we derive measures of fit and complexity (the effective number of parameters). These may be combined into a Deviance Information Criterion (DIC), which is shown to have an approximate decision-theoretic justification. Analytic and asymptotic identities reveal the measure of complexity to be a generalisation of a wide range of previous suggestions, with particular reference to the neural network literature. The contributions of individual observations to fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. The procedure is illustrated in a number of examples, and throughout it is emphasised that the required quantities are trivial to compute in a Markov chain Monte Carlo analysis, and require no analytic work for new...

This Addendum speci es additional features of BUGS 0.6, and should be read in conjunction with the current manual for BUGS 0.5 (Spiegelhalter et al., 1996a). Contents 1 Getting started 2 1.1 Getting the software.................................... 2 1.2 The script le for `bugs ' (Sparc)............................. 2

Contents 1 Getting started 2 1.1 Getting the software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The script file for `bugs' (Sparc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 The script file for `backbugs' (Sparc) . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 New Facilities in 0.6 3 2.1 Checkpoint command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Metropolis sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Minor changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Corrected bugs from Version 0.5 3 4 Known restrictions still existing in Version 0.6 4 5 Examples 4 BUGS c flcopyright MRC Biostatistics Unit 1997. ALL RIGHTS RESERVED. The support of the Economic and Social Research Council (UK) is gratefully acknowledged. The work wa